Grip shifts tend to be reasonably reliable. It is worth trying to adjust the cable tension to start with (do not adjust the little screws)(see gears section within maintenance). The screws actually adjust how far the rear mech can move so if it has worked in the past and you have not adjusted them, or banged the rear mech they should be ok.
Simply tighten/loosen the barrel adjuster until it shifts correctly. If this does not work it may be worth a trip to a decent bike mechanic.
You could change from gripshifts to rapidfire gear shifters but I would have a go with what you have to avoid any further costs.
I must admit I find gear adjustment a real pain!
Hope this helps.
